Pattern discovery is a core data mining activity. Initial approaches were dominated by the frequent pattern discovery paradigm | only frequent patterns were explored. Having been thoroughly researched and its limitations now well understood, this paradigm is giving way to two emerging alternatives - the information theoretic minimum message length paradigm and the statistically sound paradigm. This tutorial covers the latter. In this paradigm, patterns are required to pass statistical tests with respect to user defined null-hypotheses, providing great flexibility about the properties that are sought, and strict control over the risk of false discoveries and overfitting. We cover the theoretical foundations, practical issues, limitations and future directions of this growing area of research, as well as explore in detail how this approach to pattern discovery resolves many of the limitations of the frequent pattern discovery paradigm and can deliver efficient and effective discovery of small sets of interesting patterns.